Advertisements
Advertisements
प्रश्न
Find the joint equation of the pair of lines through the origin and making an equilateral triangle with the line x = 3.
Advertisements
उत्तर
Let OA and OB be the lines through the origin making an angle of 60° with the line x = 3.
∴ OA and OB make an angle of 30° and 150° with the positive direction of X-axis.
∴ Slope of OA = tan 30° = `1/sqrt3`
∴ Equation of the line OA is y = `1/sqrt3x`
∴ `sqrt3y` = x
∴ `x - sqrt3"y" = 0`
Slope of OB = tan 150°
= tan (180° – 30°)
= – tan 30°
= `- 1/sqrt3`
∴ Equation of the line OB is y = `-1/sqrt3x`
∴ `sqrt3y` = – x
∴ x + `sqrt3y` = 0
∴ Required combined equation of the lines is
`(x - sqrt3y)(x + sqrt3y)` = 0
i.e. x2 – 3y2 = 0
APPEARS IN
संबंधित प्रश्न
Find the combined equation of the following pair of lines:
2x + y = 0 and 3x − y = 0
Find the combined equation of the following pair of line:
x + 2y - 1 = 0 and x - 3y + 2 = 0
Find the combined equation of the following pair of lines:
Passing through (2, 3) and perpendicular to the lines 3x + 2y – 1 = 0 and x – 3y + 2 = 0.
Find the separate equation of the line represented by the following equation:
5x2 – 9y2 = 0
Find the separate equation of the line represented by the following equation:
`3"x"^2 - 2sqrt3"xy" - 3"y"^2 = 0`
Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by following equation:
5x2 - 8xy + 3y2 = 0
Find the combined equation of the pair of a line passing through the origin and perpendicular to the line represented by the following equation:
3x2 − 4xy = 0
Choose correct alternatives:
Auxiliary equation of 2x2 + 3xy - 9y2 = 0 is
The joint equation of the lines through the origin and perpendicular to the pair of lines 3x2 + 4xy – 5y2 = 0 is _______.
The area of triangle formed by the lines x2 + 4xy + y2 = 0 and x - y - 4 = 0 is ______.
Choose correct alternatives:
If distance between lines (x - 2y)2 + k(x - 2y) = 0 is 3 units, then k = ______.
Find the joint equation of the line passing through the origin having slopes 2 and 3.
Find the joint equation of the line passing through the origin and having inclinations 60° and 120°.
Find the joint equation of the line passing through (1, 2) and parallel to the coordinate axes
Find the joint equation of the line passing through the origin and perpendicular to the lines x + 2y = 19 and 3x + y = 18
Show that the following equations represents a pair of line:
x2 + 2xy - y2 = 0
Show that the following equations represent a pair of line:
x2 - y2 = 0
Show that the following equations represent a pair of line:
x2 + 7xy - 2y2 = 0
Show that the following equations represent a pair of line:
`"x"^2 - 2sqrt3"xy" - "y"^2 = 0`
Find the separate equation of the line represented by the following equation:
6x2 - 5xy - 6y2 = 0
Find the separate equation of the line represented by the following equation:
x2 - 4y2 = 0
Find the separate equation of the line represented by the following equation:
2x2 + 2xy - y2 = 0
Find the joint equation of the pair of a line through the origin and perpendicular to the lines given by
x2 + 4xy - 5y2 = 0
Find the joint equation of the pair of a line through the origin and perpendicular to the lines given by
2x2 - 3xy - 9y2 = 0
Find the joint equation of the pair of a line through the origin and perpendicular to the lines given by
x2 + xy - y2 = 0
Find k, if the slope of one of the lines given by 3x2 + 4xy + ky2 = 0 is three times the other.
Find the combined equation of bisectors of angles between the lines represented by 5x2 + 6xy - y2 = 0.
Find a if the sum of the slopes of lines represented by ax2 + 8xy + 5y2 = 0 is twice their product.
Show that the following equation represents a pair of line. Find the acute angle between them:
2x2 + xy - y2 + x + 4y - 3 = 0
Prove that the combined of the pair of lines passing through the origin and perpendicular to the lines ax2 + 2hxy + by2 = 0 is bx2 - 2hxy + ay2 = 0.
The joint equation of pair of lines through the origin, each of which makes an angle of 60° with Y-axis, is ______
The joint equation of the lines through the origin which forms two of the sides of the equilateral triangle having x = 2 as the third side is ______
The joint equation of pair of lines having slopes `1+sqrt2` and `1-sqrt2` and passing through the origin is ______.
The joint equation of pair of lines having slopes 2 and 5 and passing through the origin is ______.
The line 5x + y – 1 = 0 coincides with one of the lines given by 5x2 + xy – kx – 2y + 2 = 0 then the value of k is ______.
Write the joint equation of co-ordinate axes.
Combined equation of the lines bisecting the angles between the coordinate axes, is ______.
Find the joint equation of the pair of lines through the origin and perpendicular to the lines given by 2x2 + 7xy + 3y2 = 0
Find the combined equation of y-axis and the line through the origin having slope 3.
